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X₃₂₅₁¶

INTERSECTION OF X₁X_513 AND X₄₂X_663

X₃₂₅₁ = reflection of X₁₆₃₅ in X₁₉₆₀

X₃₂₅₁ (INTERSECTION OF X₁X_513 AND X₄₂X_663) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3251 = INTERSECTION OF X_1X_513 AND X_42X_663."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03251(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3251 = INTERSECTION OF X_1X_513 AND X_42X_663 on reference triangle ABC."""
            X_1635 = eval_trilinear_point(model, A, B, C, '(b - c)*(b + c - 2*a)', ID="X_1635", classes=["center"])
            X_1960 = eval_trilinear_point(model, A, B, C, 'a*(b - c)*(2*a - b - c)', ID="X_1960", classes=["center"])
            X_3251 = reflection_in_point(model, X_1635, X_1960, ID="X_3251", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_1, X_513, 1, 513, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_663 = eval_trilinear_point(model, A, B, C, 'a*(b - c)*(b + c - a)', ID="X_663", classes=["center", "incident"])
            central_line(model, X_42, X_663, 42, 663, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_667 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b - c)', ID="X_667", classes=["center", "incident"])
            central_line(model, X_55, X_667, 55, 667, incident=True)
            return promote_point_to_top(model, X_3251)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3251 on the given reference triangle."""
            model = create_model('X_3251 = INTERSECTION OF X_1X_513 AND X_42X_663')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03251(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03251.json"))
            write_center_svg(
                model_acute,
                here / "x-03251.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3251¶

X₃₂₅₁¶